%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM790+4 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:17:03 PM UTC 2026
% Result : Theorem 13.90s 3.02s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 28
% Syntax : Number of formulae : 154 ( 29 unt; 16 def)
% Number of atoms : 361 ( 2 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 352 ( 145 ~; 157 |; 20 &)
% ( 26 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 21 ( 19 usr; 17 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 10 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 78 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f190,axiom,
! [X0] :
( pp(scratc478607744_d_not(X0))
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,X0),fFalse)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__d__not) ).
fof(f191,axiom,
scratc1680081659nd_imp = fimplies,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__imp) ).
fof(f222,axiom,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1303128615all_of(X0),X1))
<=> ! [X2] :
( gg_TPTP_ind(X2)
=> ( scratc1383686962_is_of(X2,X0)
=> pp(aa_TPTP_ind_bool(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__all__of) ).
fof(f226,axiom,
pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aTP_Lamm_cg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_satz81f) ).
fof(f771,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_cg,X0))
<=> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__241) ).
fof(f774,axiom,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0))
<=> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__244) ).
fof(f855,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
<=> ( pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1)))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__325) ).
fof(f857,axiom,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,X0),X1))
<=> ( pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1)))
=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ATP_Olambda__327) ).
fof(f1280,axiom,
~ pp(fFalse),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
fof(f1281,axiom,
! [X0,X1] :
( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X0),X1))
| ~ pp(X0)
| pp(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
fof(f1283,axiom,
! [X0,X1] :
( pp(X0)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
fof(f1290,conjecture,
pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aTP_Lamm_ab)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f1291,negated_conjecture,
~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aTP_Lamm_ab)),
inference(negated_conjecture,[status(cth)],[f1290]) ).
fof(f1292,plain,
~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aTP_Lamm_ab)),
inference(flattening,[],[f1291]) ).
fof(f1309,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1303128615all_of(X0),X1))
<=> ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1383686962_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) ) ),
inference(ennf_transformation,[],[f222]) ).
fof(f1310,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1303128615all_of(X0),X1))
<=> ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1383686962_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) ) ),
inference(flattening,[],[f1309]) ).
fof(f1411,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1))
| ~ pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1))) ) ),
inference(ennf_transformation,[],[f855]) ).
fof(f1413,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,X0),X1))
<=> ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1))
| ~ pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1))) ) ),
inference(ennf_transformation,[],[f857]) ).
fof(f1708,plain,
! [X0] :
( ( pp(scratc478607744_d_not(X0))
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,X0),fFalse)) )
& ( pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,X0),fFalse))
| ~ pp(scratc478607744_d_not(X0)) ) ),
inference(nnf_transformation,[],[f190]) ).
fof(f1731,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc1303128615all_of(X0),X1))
| ? [X2] :
( ~ pp(aa_TPTP_ind_bool(X1,X2))
& scratc1383686962_is_of(X2,X0)
& gg_TPTP_ind(X2) ) )
& ( ! [X2] :
( pp(aa_TPTP_ind_bool(X1,X2))
| ~ scratc1383686962_is_of(X2,X0)
| ~ gg_TPTP_ind(X2) )
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(X0),X1)) ) ),
inference(nnf_transformation,[],[f1310]) ).
fof(f1732,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc1303128615all_of(X0),X1))
| ? [X2] :
( ~ pp(aa_TPTP_ind_bool(X1,X2))
& scratc1383686962_is_of(X2,X0)
& gg_TPTP_ind(X2) ) )
& ( ! [X3] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1383686962_is_of(X3,X0)
| ~ gg_TPTP_ind(X3) )
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(X0),X1)) ) ),
inference(rectify,[],[f1731]) ).
fof(f1733,plain,
! [X0,X1] :
( ( pp(aa_fun171081125l_bool(scratc1303128615all_of(X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(X1,sK12(X0,X1)))
& scratc1383686962_is_of(sK12(X0,X1),X0)
& gg_TPTP_ind(sK12(X0,X1)) ) )
& ( ! [X3] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1383686962_is_of(X3,X0)
| ~ gg_TPTP_ind(X3) )
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(X0),X1)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X2,sK12(X0,X1))],[f1732]) ).
fof(f1993,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_cg,X0))
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,X0))) )
& ( pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_cg,X0)) ) ),
inference(nnf_transformation,[],[f771]) ).
fof(f1996,plain,
! [X0] :
( ( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0))
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0))) )
& ( pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0)) ) ),
inference(nnf_transformation,[],[f774]) ).
fof(f2116,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1))
& pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1))) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1))
| ~ pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1)) ) ),
inference(nnf_transformation,[],[f1411]) ).
fof(f2117,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1))
& pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1))) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1))
| ~ pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1)) ) ),
inference(flattening,[],[f2116]) ).
fof(f2120,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1))
& pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1))) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1))
| ~ pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,X0),X1)) ) ),
inference(nnf_transformation,[],[f1413]) ).
fof(f2121,plain,
! [X0,X1] :
( ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,X0),X1))
| ( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1))
& pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1))) ) )
& ( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1))
| ~ pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,X0),X1)) ) ),
inference(flattening,[],[f2120]) ).
fof(f2924,plain,
! [X0] :
( pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,X0),fFalse))
| ~ pp(scratc478607744_d_not(X0)) ),
inference(cnf_transformation,[],[f1708]) ).
fof(f2925,plain,
! [X0] :
( pp(scratc478607744_d_not(X0))
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(scratc1680081659nd_imp,X0),fFalse)) ),
inference(cnf_transformation,[],[f1708]) ).
fof(f2926,plain,
scratc1680081659nd_imp = fimplies,
inference(cnf_transformation,[],[f191]) ).
fof(f2988,plain,
! [X3,X0,X1] :
( pp(aa_TPTP_ind_bool(X1,X3))
| ~ scratc1383686962_is_of(X3,X0)
| ~ gg_TPTP_ind(X3)
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(X0),X1)) ),
inference(cnf_transformation,[],[f1733]) ).
fof(f2989,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1303128615all_of(X0),X1))
| gg_TPTP_ind(sK12(X0,X1)) ),
inference(cnf_transformation,[],[f1733]) ).
fof(f2990,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1303128615all_of(X0),X1))
| scratc1383686962_is_of(sK12(X0,X1),X0) ),
inference(cnf_transformation,[],[f1733]) ).
fof(f2991,plain,
! [X0,X1] :
( pp(aa_fun171081125l_bool(scratc1303128615all_of(X0),X1))
| ~ pp(aa_TPTP_ind_bool(X1,sK12(X0,X1))) ),
inference(cnf_transformation,[],[f1733]) ).
fof(f2996,plain,
pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aTP_Lamm_cg)),
inference(cnf_transformation,[],[f226]) ).
fof(f3811,plain,
! [X0] :
( pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,X0)))
| ~ pp(aa_TPTP_ind_bool(aTP_Lamm_cg,X0)) ),
inference(cnf_transformation,[],[f1993]) ).
fof(f3818,plain,
! [X0] :
( pp(aa_TPTP_ind_bool(aTP_Lamm_ab,X0))
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,X0))) ),
inference(cnf_transformation,[],[f1996]) ).
fof(f4017,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1))) ),
inference(cnf_transformation,[],[f2117]) ).
fof(f4018,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,X0),X1))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1)) ),
inference(cnf_transformation,[],[f2117]) ).
fof(f4022,plain,
! [X0,X1] :
( pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,X0),X1))
| ~ pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,X0),X1)))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,X0),X1)) ),
inference(cnf_transformation,[],[f2121]) ).
fof(f5080,plain,
~ pp(fFalse),
inference(cnf_transformation,[],[f1280]) ).
fof(f5081,plain,
! [X0,X1] :
( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X0),X1))
| ~ pp(X0)
| pp(X1) ),
inference(cnf_transformation,[],[f1281]) ).
fof(f5083,plain,
! [X0,X1] :
( pp(X0)
| pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X0),X1)) ),
inference(cnf_transformation,[],[f1283]) ).
fof(f5090,plain,
~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aTP_Lamm_ab)),
inference(cnf_transformation,[],[f1292]) ).
fof(f5190,plain,
! [X0] :
( pp(scratc478607744_d_not(X0))
| ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X0),fFalse)) ),
inference(definition_unfolding,[],[f2925,f2926]) ).
fof(f5191,plain,
! [X0] :
( pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,X0),fFalse))
| ~ pp(scratc478607744_d_not(X0)) ),
inference(definition_unfolding,[],[f2924,f2926]) ).
fof(f5450,definition,
( spl29_1
<=> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aTP_Lamm_ab)) ),
introduced(definition,[new_symbols(definition,[spl29_1])],[avatar_definition]) ).
fof(f5452,plain,
( ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aTP_Lamm_ab))
| spl29_1 ),
inference(avatar_component_clause,[],[f5450]) ).
fof(f5453,plain,
~ spl29_1,
inference(avatar_split_clause,[],[f5090,f5450]) ).
fof(f5454,plain,
( gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_ab))
| spl29_1 ),
inference(resolution,[],[f5452,f2989]) ).
fof(f5455,plain,
( scratc1383686962_is_of(sK12(aTP_Lamm_a,aTP_Lamm_ab),aTP_Lamm_a)
| spl29_1 ),
inference(resolution,[],[f5452,f2990]) ).
fof(f5456,plain,
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_1 ),
inference(resolution,[],[f5452,f2991]) ).
fof(f5469,definition,
( spl29_2
<=> scratc1383686962_is_of(sK12(aTP_Lamm_a,aTP_Lamm_ab),aTP_Lamm_a) ),
introduced(definition,[new_symbols(definition,[spl29_2])],[avatar_definition]) ).
fof(f5471,plain,
( scratc1383686962_is_of(sK12(aTP_Lamm_a,aTP_Lamm_ab),aTP_Lamm_a)
| ~ spl29_2 ),
inference(avatar_component_clause,[],[f5469]) ).
fof(f5472,plain,
( spl29_2
| spl29_1 ),
inference(avatar_split_clause,[],[f5455,f5450,f5469]) ).
fof(f5474,definition,
( spl29_3
<=> gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_ab)) ),
introduced(definition,[new_symbols(definition,[spl29_3])],[avatar_definition]) ).
fof(f5476,plain,
( gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_ab))
| ~ spl29_3 ),
inference(avatar_component_clause,[],[f5474]) ).
fof(f5477,plain,
( spl29_3
| spl29_1 ),
inference(avatar_split_clause,[],[f5454,f5450,f5474]) ).
fof(f5479,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ gg_TPTP_ind(sK12(aTP_Lamm_a,aTP_Lamm_ab))
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),X0)) )
| ~ spl29_2 ),
inference(resolution,[],[f5471,f2988]) ).
fof(f5480,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),X0)) )
| ~ spl29_2
| ~ spl29_3 ),
inference(forward_subsumption_resolution,[],[f5479,f5476]) ).
fof(f5482,definition,
( spl29_4
<=> ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl29_4])],[avatar_definition]) ).
fof(f5483,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),X0)) )
| ~ spl29_4 ),
inference(avatar_component_clause,[],[f5482]) ).
fof(f5484,plain,
( spl29_4
| ~ spl29_2
| ~ spl29_3 ),
inference(avatar_split_clause,[],[f5480,f5474,f5469,f5482]) ).
fof(f6420,plain,
( ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aTP_Lamm_cg))
| pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_4 ),
inference(resolution,[],[f5483,f3811]) ).
fof(f6688,plain,
( pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_4 ),
inference(forward_subsumption_resolution,[],[f6420,f2996]) ).
fof(f6811,definition,
( spl29_5
<=> pp(aa_TPTP_ind_bool(aTP_Lamm_ab,sK12(aTP_Lamm_a,aTP_Lamm_ab))) ),
introduced(definition,[new_symbols(definition,[spl29_5])],[avatar_definition]) ).
fof(f6813,plain,
( ~ pp(aa_TPTP_ind_bool(aTP_Lamm_ab,sK12(aTP_Lamm_a,aTP_Lamm_ab)))
| spl29_5 ),
inference(avatar_component_clause,[],[f6811]) ).
fof(f6814,plain,
( ~ spl29_5
| spl29_1 ),
inference(avatar_split_clause,[],[f5456,f5450,f6811]) ).
fof(f6815,plain,
( ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| spl29_5 ),
inference(resolution,[],[f6813,f3818]) ).
fof(f6854,definition,
( spl29_6
<=> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))) ),
introduced(definition,[new_symbols(definition,[spl29_6])],[avatar_definition]) ).
fof(f6856,plain,
( ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| spl29_6 ),
inference(avatar_component_clause,[],[f6854]) ).
fof(f6857,plain,
( ~ spl29_6
| spl29_5 ),
inference(avatar_split_clause,[],[f6815,f6811,f6854]) ).
fof(f6859,plain,
( gg_TPTP_ind(sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| spl29_6 ),
inference(resolution,[],[f6856,f2989]) ).
fof(f6860,plain,
( scratc1383686962_is_of(sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))),aTP_Lamm_a)
| spl29_6 ),
inference(resolution,[],[f6856,f2990]) ).
fof(f6861,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| spl29_6 ),
inference(resolution,[],[f6856,f2991]) ).
fof(f6874,definition,
( spl29_7
<=> scratc1383686962_is_of(sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))),aTP_Lamm_a) ),
introduced(definition,[new_symbols(definition,[spl29_7])],[avatar_definition]) ).
fof(f6876,plain,
( scratc1383686962_is_of(sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))),aTP_Lamm_a)
| ~ spl29_7 ),
inference(avatar_component_clause,[],[f6874]) ).
fof(f6877,plain,
( spl29_7
| spl29_6 ),
inference(avatar_split_clause,[],[f6860,f6854,f6874]) ).
fof(f6879,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| ~ gg_TPTP_ind(sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),X0)) )
| ~ spl29_7 ),
inference(resolution,[],[f6876,f2988]) ).
fof(f6880,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),X0)) )
| spl29_6
| ~ spl29_7 ),
inference(forward_subsumption_resolution,[],[f6879,f6859]) ).
fof(f6882,definition,
( spl29_8
<=> ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),X0)) ) ),
introduced(definition,[new_symbols(definition,[spl29_8])],[avatar_definition]) ).
fof(f6883,plain,
( ! [X0] :
( pp(aa_TPTP_ind_bool(X0,sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),X0)) )
| ~ spl29_8 ),
inference(avatar_component_clause,[],[f6882]) ).
fof(f6884,plain,
( spl29_8
| spl29_6
| ~ spl29_7 ),
inference(avatar_split_clause,[],[f6880,f6874,f6854,f6882]) ).
fof(f8211,definition,
( spl29_9
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))) ),
introduced(definition,[new_symbols(definition,[spl29_9])],[avatar_definition]) ).
fof(f8213,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| spl29_9 ),
inference(avatar_component_clause,[],[f8211]) ).
fof(f8214,plain,
( ~ spl29_9
| spl29_6 ),
inference(avatar_split_clause,[],[f6861,f6854,f8211]) ).
fof(f8215,plain,
( pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| spl29_9 ),
inference(resolution,[],[f8213,f4017]) ).
fof(f8216,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| spl29_9 ),
inference(resolution,[],[f8213,f4018]) ).
fof(f8268,definition,
( spl29_11
<=> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))) ),
introduced(definition,[new_symbols(definition,[spl29_11])],[avatar_definition]) ).
fof(f8270,plain,
( pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| ~ spl29_11 ),
inference(avatar_component_clause,[],[f8268]) ).
fof(f8271,plain,
( spl29_11
| spl29_9 ),
inference(avatar_split_clause,[],[f8215,f8211,f8268]) ).
fof(f8275,plain,
( pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),fFalse))
| ~ spl29_11 ),
inference(resolution,[],[f8270,f5191]) ).
fof(f8286,definition,
( spl29_12
<=> pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),fFalse)) ),
introduced(definition,[new_symbols(definition,[spl29_12])],[avatar_definition]) ).
fof(f8288,plain,
( pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),fFalse))
| ~ spl29_12 ),
inference(avatar_component_clause,[],[f8286]) ).
fof(f8289,plain,
( spl29_12
| ~ spl29_11 ),
inference(avatar_split_clause,[],[f8275,f8268,f8286]) ).
fof(f8291,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| pp(fFalse)
| ~ spl29_12 ),
inference(resolution,[],[f8288,f5081]) ).
fof(f8302,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| ~ spl29_12 ),
inference(forward_subsumption_resolution,[],[f8291,f5080]) ).
fof(f8308,definition,
( spl29_14
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))) ),
introduced(definition,[new_symbols(definition,[spl29_14])],[avatar_definition]) ).
fof(f8310,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc380388658moreis,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| spl29_14 ),
inference(avatar_component_clause,[],[f8308]) ).
fof(f8311,plain,
( ~ spl29_14
| ~ spl29_12 ),
inference(avatar_split_clause,[],[f8302,f8286,f8308]) ).
fof(f8316,definition,
( spl29_15
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))) ),
introduced(definition,[new_symbols(definition,[spl29_15])],[avatar_definition]) ).
fof(f8318,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| spl29_15 ),
inference(avatar_component_clause,[],[f8316]) ).
fof(f8319,plain,
( ~ spl29_15
| spl29_9 ),
inference(avatar_split_clause,[],[f8216,f8211,f8316]) ).
fof(f8362,plain,
( ! [X0] : pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),X0))
| spl29_15 ),
inference(resolution,[],[f8318,f5083]) ).
fof(f8565,plain,
( ~ pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| spl29_14 ),
inference(resolution,[],[f8310,f4022]) ).
fof(f9005,definition,
( spl29_34
<=> pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))) ),
introduced(definition,[new_symbols(definition,[spl29_34])],[avatar_definition]) ).
fof(f9007,plain,
( ~ pp(aa_TPTP_ind_bool(aa_TPT43085870d_bool(aTP_Lamm_cf,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))
| spl29_34 ),
inference(avatar_component_clause,[],[f9005]) ).
fof(f9009,definition,
( spl29_35
<=> pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab)))))) ),
introduced(definition,[new_symbols(definition,[spl29_35])],[avatar_definition]) ).
fof(f9011,plain,
( ~ pp(scratc478607744_d_not(aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))))
| spl29_35 ),
inference(avatar_component_clause,[],[f9009]) ).
fof(f9012,plain,
( ~ spl29_34
| ~ spl29_35
| spl29_14 ),
inference(avatar_split_clause,[],[f8565,f8308,f9009,f9005]) ).
fof(f9432,definition,
( spl29_56
<=> pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,sK12(aTP_Lamm_a,aTP_Lamm_ab)))) ),
introduced(definition,[new_symbols(definition,[spl29_56])],[avatar_definition]) ).
fof(f9434,plain,
( pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_56 ),
inference(avatar_component_clause,[],[f9432]) ).
fof(f9435,plain,
( spl29_56
| ~ spl29_4 ),
inference(avatar_split_clause,[],[f6688,f5482,f9432]) ).
fof(f9644,plain,
( ~ pp(aa_fun171081125l_bool(scratc1303128615all_of(aTP_Lamm_a),aa_TPT43085870d_bool(aTP_Lamm_cf,sK12(aTP_Lamm_a,aTP_Lamm_ab))))
| ~ spl29_8
| spl29_34 ),
inference(resolution,[],[f9007,f6883]) ).
fof(f9684,plain,
( $false
| ~ spl29_8
| spl29_34
| ~ spl29_56 ),
inference(forward_subsumption_resolution,[],[f9644,f9434]) ).
fof(f9685,plain,
( ~ spl29_8
| spl29_34
| ~ spl29_56 ),
inference(avatar_contradiction_clause,[],[f9684]) ).
fof(f9689,plain,
( ~ pp(aa_bool_bool(aa_boo1142376798l_bool(fimplies,aa_TPTP_ind_bool(aa_TPT43085870d_bool(scratc79803244t_less,sK12(aTP_Lamm_a,aTP_Lamm_ab)),sK12(aTP_Lamm_a,aa_TPT43085870d_bool(aTP_Lamm_aa,sK12(aTP_Lamm_a,aTP_Lamm_ab))))),fFalse))
| spl29_35 ),
inference(resolution,[],[f9011,f5190]) ).
fof(f9702,plain,
( $false
| spl29_15
| spl29_35 ),
inference(forward_subsumption_resolution,[],[f9689,f8362]) ).
fof(f9703,plain,
( spl29_15
| spl29_35 ),
inference(avatar_contradiction_clause,[],[f9702]) ).
cnf(s1,plain,
~ spl29_1,
inference(sat_conversion,[],[f5453]) ).
cnf(s2,plain,
( spl29_1
| spl29_2 ),
inference(sat_conversion,[],[f5472]) ).
cnf(s3,plain,
( spl29_1
| spl29_3 ),
inference(sat_conversion,[],[f5477]) ).
cnf(s4,plain,
( ~ spl29_2
| ~ spl29_3
| spl29_4 ),
inference(sat_conversion,[],[f5484]) ).
cnf(s5,plain,
( spl29_1
| ~ spl29_5 ),
inference(sat_conversion,[],[f6814]) ).
cnf(s6,plain,
( spl29_5
| ~ spl29_6 ),
inference(sat_conversion,[],[f6857]) ).
cnf(s7,plain,
( spl29_6
| spl29_7 ),
inference(sat_conversion,[],[f6877]) ).
cnf(s8,plain,
( spl29_6
| ~ spl29_7
| spl29_8 ),
inference(sat_conversion,[],[f6884]) ).
cnf(s9,plain,
( spl29_6
| ~ spl29_9 ),
inference(sat_conversion,[],[f8214]) ).
cnf(s11,plain,
( spl29_9
| spl29_11 ),
inference(sat_conversion,[],[f8271]) ).
cnf(s12,plain,
( ~ spl29_11
| spl29_12 ),
inference(sat_conversion,[],[f8289]) ).
cnf(s14,plain,
( ~ spl29_12
| ~ spl29_14 ),
inference(sat_conversion,[],[f8311]) ).
cnf(s15,plain,
( spl29_9
| ~ spl29_15 ),
inference(sat_conversion,[],[f8319]) ).
cnf(s34,plain,
( spl29_14
| ~ spl29_34
| ~ spl29_35 ),
inference(sat_conversion,[],[f9012]) ).
cnf(s55,plain,
( ~ spl29_4
| spl29_56 ),
inference(sat_conversion,[],[f9435]) ).
cnf(s65,plain,
( ~ spl29_8
| spl29_34
| ~ spl29_56 ),
inference(sat_conversion,[],[f9685]) ).
cnf(s66,plain,
( spl29_15
| spl29_35 ),
inference(sat_conversion,[],[f9703]) ).
cnf(s67,plain,
~ spl29_5,
inference(rat,[],[s5,s1]) ).
cnf(s68,plain,
spl29_3,
inference(rat,[],[s3,s1]) ).
cnf(s69,plain,
spl29_2,
inference(rat,[],[s2,s1]) ).
cnf(s71,plain,
~ spl29_6,
inference(rat,[],[s6,s67]) ).
cnf(s75,plain,
spl29_4,
inference(rat,[],[s4,s68,s69]) ).
cnf(s78,plain,
~ spl29_9,
inference(rat,[],[s9,s71]) ).
cnf(s79,plain,
spl29_7,
inference(rat,[],[s7,s71]) ).
cnf(s88,plain,
spl29_56,
inference(rat,[],[s55,s75]) ).
cnf(s96,plain,
~ spl29_15,
inference(rat,[],[s15,s78]) ).
cnf(s98,plain,
spl29_11,
inference(rat,[],[s11,s78]) ).
cnf(s99,plain,
spl29_8,
inference(rat,[],[s8,s71,s79]) ).
cnf(s100,plain,
spl29_35,
inference(rat,[],[s66,s96]) ).
cnf(s104,plain,
spl29_12,
inference(rat,[],[s12,s98]) ).
cnf(s105,plain,
spl29_34,
inference(rat,[],[s65,s88,s99]) ).
cnf(s123,plain,
~ spl29_14,
inference(rat,[],[s14,s104]) ).
cnf(s124,plain,
$false,
inference(rat,[],[s34,s100,s105,s123]) ).
fof(f9704,plain,
$false,
inference(avatar_sat_refutation,[],[s124]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM790+4 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n016.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 21:30:29 UTC 2026
% 0.14/0.37 % CPUTime :
% 0.14/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 Running first-order theorem proving
% 0.14/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 12.89/2.71 % (3006679)Detected formulas, will run a generic FOF schedule.
% 12.89/2.71 % (3006686)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=3383423362:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 12.89/2.71 % (3006688)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1291305581:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 12.89/2.71 % (3006690)dis-21_1_sil=8000:lcm=predicate:random_seed=2696331451:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 12.89/2.71 % (3006687)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2271923253:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 12.89/2.71 % (3006684)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2481479119:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 12.89/2.71 % (3006685)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3366002063:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 12.89/2.71 % (3006687)Refutation not found, incomplete strategy
% 12.89/2.71 % (3006687)------------------------------
% 12.89/2.71 % (3006687)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.89/2.71 % (3006687)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.89/2.71 % (3006687)CaDiCaL version: 2.1.3
% 12.89/2.71 % (3006687)Termination reason: Refutation not found, incomplete strategy
% 12.89/2.71 % (3006687)Time elapsed: 0.005 s
% 12.89/2.71 % (3006687)Peak memory usage: 89 MB
% 12.89/2.71 % (3006687)Instructions burned: 6 (million)
% 12.89/2.71 % (3006688)Refutation not found, incomplete strategy
% 12.89/2.71 % (3006688)------------------------------
% 12.89/2.71 % (3006688)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.89/2.71 % (3006688)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.89/2.71 % (3006688)CaDiCaL version: 2.1.3
% 12.89/2.71 % (3006688)Termination reason: Refutation not found, incomplete strategy
% 12.89/2.71 % (3006688)Time elapsed: 0.005 s
% 12.89/2.71 % (3006688)Peak memory usage: 89 MB
% 12.89/2.71 % (3006688)Instructions burned: 7 (million)
% 12.89/2.71 % (3006689)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=509733617:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 12.89/2.71 % (3006690)Instruction limit reached!
% 12.89/2.71 % (3006690)------------------------------
% 12.89/2.71 % (3006690)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.89/2.71 % (3006690)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.89/2.71 % (3006690)CaDiCaL version: 2.1.3
% 12.89/2.71 % (3006690)Termination reason: Instruction limit
% 12.89/2.71 % (3006690)Termination phase: Saturation
% 12.89/2.71 % (3006690)Time elapsed: 0.055 s
% 12.89/2.71 % (3006690)Peak memory usage: 90 MB
% 12.89/2.71 % (3006690)Instructions burned: 129 (million)
% 12.89/2.71 % (3006689)Instruction limit reached!
% 12.89/2.71 % (3006689)------------------------------
% 12.89/2.71 % (3006689)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.89/2.71 % (3006689)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.89/2.71 % (3006689)CaDiCaL version: 2.1.3
% 12.89/2.71 % (3006689)Termination reason: Instruction limit
% 12.89/2.71 % (3006689)Termination phase: Saturation
% 12.89/2.71 % (3006689)Time elapsed: 0.061 s
% 12.89/2.71 % (3006689)Peak memory usage: 90 MB
% 12.89/2.71 % (3006689)Instructions burned: 139 (million)
% 12.89/2.71 % (3006698)lrs+10_1_sil=8000:sp=occurrence:random_seed=306615086:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 12.89/2.71 % (3006698)Refutation not found, incomplete strategy
% 12.89/2.71 % (3006698)------------------------------
% 12.89/2.71 % (3006698)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 12.89/2.71 % (3006698)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 12.89/2.71 % (3006698)CaDiCaL version: 2.1.3
% 12.89/2.71 % (3006698)Termination reason: Refutation not found, incomplete strategy
% 12.89/2.71 % (3006698)Time elapsed: 0.005 s
% 12.89/2.71 % (3006698)Peak memory usage: 89 MB
% 12.89/2.71 % (3006698)Instructions burned: 6 (million)
% 12.89/2.71 % (3006699)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2586501113:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 13.90/3.02 % (3006699)Refutation not found, incomplete strategy
% 13.90/3.02 % (3006699)------------------------------
% 13.90/3.02 % (3006699)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/3.02 % (3006699)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/3.02 % (3006699)CaDiCaL version: 2.1.3
% 13.90/3.02 % (3006699)Termination reason: Refutation not found, incomplete strategy
% 13.90/3.02 % (3006699)Time elapsed: 0.010 s
% 13.90/3.02 % (3006699)Peak memory usage: 89 MB
% 13.90/3.02 % (3006699)Instructions burned: 21 (million)
% 13.90/3.02 % (3006688)------------------------------
% 13.90/3.02 % (3006688)------------------------------
% 13.90/3.02 % (3006687)------------------------------
% 13.90/3.02 % (3006687)------------------------------
% 13.90/3.02 % (3006702)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1584201874:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 13.90/3.02 % (3006703)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1288997731:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 13.90/3.02 % (3006702)Refutation not found, incomplete strategy
% 13.90/3.02 % (3006702)------------------------------
% 13.90/3.02 % (3006702)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/3.02 % (3006702)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/3.02 % (3006702)CaDiCaL version: 2.1.3
% 13.90/3.02 % (3006702)Termination reason: Refutation not found, incomplete strategy
% 13.90/3.02 % (3006702)Time elapsed: 0.010 s
% 13.90/3.02 % (3006702)Peak memory usage: 90 MB
% 13.90/3.02 % (3006702)Instructions burned: 14 (million)
% 13.90/3.02 % (3006698)------------------------------
% 13.90/3.02 % (3006698)------------------------------
% 13.90/3.02 % (3006699)------------------------------
% 13.90/3.02 % (3006699)------------------------------
% 13.90/3.02 % (3006703)Instruction limit reached!
% 13.90/3.02 % (3006703)------------------------------
% 13.90/3.02 % (3006703)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/3.02 % (3006703)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/3.02 % (3006703)CaDiCaL version: 2.1.3
% 13.90/3.02 % (3006703)Termination reason: Instruction limit
% 13.90/3.02 % (3006703)Termination phase: Saturation
% 13.90/3.02 % (3006703)Time elapsed: 0.130 s
% 13.90/3.02 % (3006703)Peak memory usage: 96 MB
% 13.90/3.02 % (3006703)Instructions burned: 249 (million)
% 13.90/3.02 % (3006706)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1663530333:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2993 on theBenchmark for (2993ds/294Mi)
% 13.90/3.02 % (3006706)Refutation not found, incomplete strategy
% 13.90/3.02 % (3006706)------------------------------
% 13.90/3.02 % (3006706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/3.02 % (3006706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/3.02 % (3006706)CaDiCaL version: 2.1.3
% 13.90/3.02 % (3006706)Termination reason: Refutation not found, incomplete strategy
% 13.90/3.02 % (3006706)Time elapsed: 0.010 s
% 13.90/3.02 % (3006706)Peak memory usage: 90 MB
% 13.90/3.02 % (3006706)Instructions burned: 15 (million)
% 13.90/3.02 % (3006707)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2432819089:i=2350_2993 on theBenchmark for (2993ds/2350Mi)
% 13.90/3.02 % (3006702)------------------------------
% 13.90/3.02 % (3006702)------------------------------
% 13.90/3.02 % (3006708)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2487285124:cts=off:i=113:fsr=off:ss=included:sgt=4_2992 on theBenchmark for (2992ds/113Mi)
% 13.90/3.02 % (3006708)Instruction limit reached!
% 13.90/3.02 % (3006708)------------------------------
% 13.90/3.02 % (3006708)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/3.02 % (3006708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/3.02 % (3006708)CaDiCaL version: 2.1.3
% 13.90/3.02 % (3006708)Termination reason: Instruction limit
% 13.90/3.02 % (3006708)Termination phase: Saturation
% 13.90/3.02 % (3006708)Time elapsed: 0.055 s
% 13.90/3.02 % (3006708)Peak memory usage: 90 MB
% 13.90/3.02 % (3006708)Instructions burned: 115 (million)
% 13.90/3.02 % (3006711)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=2885241620:i=127:av=off:fsr=off:sup=off_2991 on theBenchmark for (2991ds/127Mi)
% 13.90/3.02 % (3006706)------------------------------
% 13.90/3.02 % (3006706)------------------------------
% 13.90/3.02 % (3006711)Instruction limit reached!
% 13.90/3.02 % (3006711)------------------------------
% 13.90/3.02 % (3006711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/3.02 % (3006711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/3.02 % (3006711)CaDiCaL version: 2.1.3
% 13.90/3.02 % (3006711)Termination reason: Instruction limit
% 13.90/3.02 % (3006711)Termination phase: Property scanning
% 13.90/3.02 % (3006711)Time elapsed: 0.056 s
% 13.90/3.02 % (3006711)Peak memory usage: 89 MB
% 13.90/3.02 % (3006711)Instructions burned: 129 (million)
% 13.90/3.02 % (3006713)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=2623827510:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2990 on theBenchmark for (2990ds/114Mi)
% 13.90/3.02 % (3006713)Instruction limit reached!
% 13.90/3.02 % (3006713)------------------------------
% 13.90/3.02 % (3006713)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/3.02 % (3006713)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/3.02 % (3006713)CaDiCaL version: 2.1.3
% 13.90/3.02 % (3006713)Termination reason: Instruction limit
% 13.90/3.02 % (3006713)Termination phase: Saturation
% 13.90/3.02 % (3006713)Time elapsed: 0.058 s
% 13.90/3.02 % (3006713)Peak memory usage: 90 MB
% 13.90/3.02 % (3006713)Instructions burned: 114 (million)
% 13.90/3.02 % (3006715)lrs+10_1_sil=8000:sp=occurrence:random_seed=2353166153:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2989 on theBenchmark for (2989ds/907Mi)
% 13.90/3.02 % (3006716)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3333167572:i=437:sd=1:aac=none:ss=included_2989 on theBenchmark for (2989ds/437Mi)
% 13.90/3.02 % (3006718)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=173166030:i=5202:ss=axioms:sgt=16_2988 on theBenchmark for (2988ds/5202Mi)
% 13.90/3.02 % (3006716)Refutation not found, incomplete strategy
% 13.90/3.02 % (3006716)------------------------------
% 13.90/3.02 % (3006716)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/3.02 % (3006716)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/3.02 % (3006716)CaDiCaL version: 2.1.3
% 13.90/3.02 % (3006716)Termination reason: Refutation not found, incomplete strategy
% 13.90/3.02 % (3006716)Time elapsed: 0.094 s
% 13.90/3.02 % (3006716)Peak memory usage: 93 MB
% 13.90/3.02 % (3006716)Instructions burned: 192 (million)
% 13.90/3.02 % (3006716)------------------------------
% 13.90/3.02 % (3006716)------------------------------
% 13.90/3.02 % (3006722)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=1271673855:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2984 on theBenchmark for (2984ds/134Mi)
% 13.90/3.02 % (3006722)Instruction limit reached!
% 13.90/3.02 % (3006722)------------------------------
% 13.90/3.02 % (3006722)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/3.02 % (3006722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/3.02 % (3006722)CaDiCaL version: 2.1.3
% 13.90/3.02 % (3006722)Termination reason: Instruction limit
% 13.90/3.02 % (3006722)Termination phase: Saturation
% 13.90/3.02 % (3006722)Time elapsed: 0.061 s
% 13.90/3.02 % (3006722)Peak memory usage: 91 MB
% 13.90/3.02 % (3006722)Instructions burned: 135 (million)
% 13.90/3.02 % (3006715)Instruction limit reached!
% 13.90/3.02 % (3006715)------------------------------
% 13.90/3.02 % (3006715)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/3.02 % (3006715)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/3.02 % (3006715)CaDiCaL version: 2.1.3
% 13.90/3.02 % (3006715)Termination reason: Instruction limit
% 13.90/3.02 % (3006715)Termination phase: Saturation
% 13.90/3.02 % (3006715)Time elapsed: 0.545 s
% 13.90/3.02 % (3006715)Peak memory usage: 102 MB
% 13.90/3.02 % (3006715)Instructions burned: 910 (million)
% 13.90/3.02 % (3006724)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=698209417:st=8:i=592:sd=3:ep=RST:ss=axioms_2982 on theBenchmark for (2982ds/592Mi)
% 13.90/3.02 % (3006725)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=2020979350:st=3:i=13193:sd=3:ss=axioms_2982 on theBenchmark for (2982ds/13193Mi)
% 13.90/3.02 % (3006724)Refutation not found, incomplete strategy
% 13.90/3.02 % (3006724)------------------------------
% 13.90/3.02 % (3006724)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 13.90/3.02 % (3006724)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 13.90/3.02 % (3006724)CaDiCaL version: 2.1.3
% 13.90/3.02 % (3006724)Termination reason: Refutation not found, incomplete strategy
% 13.90/3.02 % (3006724)Time elapsed: 0.021 s
% 13.90/3.02 % (3006724)Peak memory usage: 90 MB
% 13.90/3.02 % (3006724)Instructions burned: 40 (million)
% 13.90/3.02 % (3006686)First to succeed.
% 13.90/3.02 % (3006686)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3006679"
% 13.90/3.02 % (3006724)------------------------------
% 13.90/3.02 % (3006724)------------------------------
% 13.90/3.02 % (3006686)Refutation found. Thanks to Tanya!
% 13.90/3.02 % SZS status Theorem for theBenchmark
% 13.90/3.02 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/3.21 % (3006686)------------------------------
% 0.16/3.21 % (3006686)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/3.21 % (3006686)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/3.21 % (3006686)CaDiCaL version: 2.1.3
% 0.16/3.21 % (3006686)Termination reason: Refutation
% 0.16/3.21 % (3006686)Time elapsed: 1.707 s
% 0.16/3.21 % (3006686)Peak memory usage: 161 MB
% 0.16/3.21 % (3006686)Instructions burned: 3449 (million)
% 0.16/3.21 % (3006686)------------------------------
% 0.16/3.21 % (3006686)------------------------------
% 0.16/3.21 % (3006679)Success in time 2.167 s
% 0.16/3.21 % Vampire exiting
%------------------------------------------------------------------------------